Finite Group Databasebeta

← #14326316

Subgroups — #14326316

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#217C211yesmaximal, characteristic
2C22×#6665C211yesmaximal, characteristic
3C2×#91393C211yesmaximal, characteristic, complemented
4#11751047C211yesmaximal, characteristic, complemented
5C5×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#65244C211yesmaximal, characteristic
7#11749512C211yesmaximal, characteristic, complemented
8#11749487C211yesmaximal, characteristic, complemented
9#11748885C211yesmaximal, characteristic, complemented
10Dic3×#685C211yesmaximal, characteristic, complemented
11#11748871C211yesmaximal, characteristic, complemented
12#11748708C211yesmaximal, characteristic, complemented
13#11748707C211yesmaximal, characteristic, complemented
14#11748706C211yesmaximal, characteristic, complemented
15#11748705C211yesmaximal, characteristic, complemented
16#10605305—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6712C2211yescharacteristic, complemented
25C2×#6712C2211yescharacteristic, complemented
26C2×C5×#217C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic, complemented
28C2×C4×C5×Dic3C2211yescharacteristic, complemented
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34D5×#217C418yescomplemented
35C2×#6669C2211yescharacteristic, complemented
36C2×#6669C2211yescharacteristic, complemented
37C2×#6665—24no—
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91393—24no—
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#73822—51nomaximal, Hall
56C22×#685—31no—
57C2×D5×C22⋊C4—31no—
58C2×#4018—31no—
59C4×C5×C22⋊C4—31no—
60#65499—31no—
61#65244D311yescharacteristic
62#65235—31no—
63C22⋊C4×Dic5—31no—
64#65229—31no—
65#65229—31no—
66C4×#685—31no—
67#64958—31no—
68#64958—31no—
69#64956—31no—
70#64953—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5—22no—
73C23×C3×D5—22no—
74C23×C3×D5—22no—
75C23×C3×D5—22no—
76C23×C3×D5—41no—
77C23×C3×D5—41no—
78C23×C3×D5C2×C414yes—
79C23×C3×D5C2311yescharacteristic
80C23×C3×D5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15—22no—
84C22×Dic15—22no—
85C22×Dic15—41no—
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×C5×Dic3—22no—
91C22×C5×Dic3—22no—
92C22×C5×Dic3—41no—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×D5×Dic3—22no—
100C2×D5×Dic3—22no—
101C2×D5×Dic3—41no—
102C2×D5×Dic3—41no—
103C2×D5×Dic3C2×C414yescomplemented
104C2×D5×Dic3C2×C414yescomplemented
105C3×C5×C22⋊C4—22no—
106#6719C2×C414yes—
107#6712—22no—
108#6712—41no—
109C5×#217C2×C414yes—
110C4×C5×Dic3—22no—
111C4×C5×Dic3—41no—
112C3×C22⋊Dic5—22no—
113C3×#685—22no—
114C3×#685—22no—
115C3×#685—41no—
116C3×#685—41no—
117#6669—22no—
118#6669—41no—
119#6665—22no—
120#6665—22no—
121#6665—22no—
122#6665C2×C414yescomplemented
123#6665C2×C414yescomplemented
124#6665D414yes—
125Dic3×Dic5—22no—
126Dic3×Dic5—41no—
127C22×#217—51no—
128C22×#217—51no—
129C2×#877—51no—
130C3×#379—51no—
131#4946—51no—
132#4946—51no—
133#4945—51no—
134#4945—51no—
135#4944—51no—
136#4944—51no—
137#4943—51no—
138#4942—51no—
139Dic3×C22⋊C4—51no—
140Dic3×C22⋊C4—51no—
141Dic3×C22⋊C4D511yescharacteristic, complemented
142C24×D5C2×D311yescharacteristic
143C23×C4×C5—31no—
144C23×Dic5—31no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C2×C5×C22⋊C4—31no—
148C2×C5×C22⋊C4C2×D311yescharacteristic
149C2×C42×C5—31no—
150C2×C42×C5—31no—
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5C2×D311yescharacteristic
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—64no—
160C2×#685C2×D311yescharacteristic
161C2×#685C2×D311yescharacteristic
162C2×#685C2×D311yescharacteristic
163C2×#685C2×D311yescharacteristic
164C2×#683—31no—
165C2×#683—31no—
166C2×#683—31no—
167C2×#683—31no—
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170D5×C22⋊C4—38no—
171#4018—64no—
172C5×#95—31no—
173C5×#95—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2342—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5#4112yes—
187C23×C3×C5#4112yes—
188C23×C3×C5C2411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—28no—
194C22×C3×D5—21no—
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—28no—
201C22×C3×D5—44no—
202C22×C3×D5—44no—
203C22×C3×D5—44no—
204C22×C3×D5—44no—
205C22×C3×D5—44no—
206C22×C3×D5C22×C412yes—
207C22×C3×D5C22×C412yes—
208C22×C3×D5C2×D412yes—
209C22×C3×D5#4112yes—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—44no—
226C2×Dic15C22×C412yes—
227C2×Dic15C22×C412yes—
228C2×Dic15C2×D412yes—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—44no—
239C2×C5×Dic3C22×C412yes—
240C2×C5×Dic3C22×C412yes—
241C2×C5×Dic3C2×D412yes—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248D5×Dic3—28no—
249D5×Dic3—44no—
250C25×C3—51no—
251C23×Dic3—51no—
252C23×Dic3—51no—
253C23×Dic3—51no—
254C23×Dic3C2×D511yescharacteristic
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4C2×D511yescharacteristic
261C2×#217—51no—
262C2×#217—51no—
263C2×#217—51no—
264C2×#217—51no—
265C2×#217—58no—
266C2×#217—51no—
267C2×#217—51no—
268C2×#217—51no—
269C2×#217—104no—
270C2×#217C2×D511yescharacteristic
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277C2×C4×Dic3C2×D511yescharacteristic, complemented
278C2×C4×Dic3C2×D511yescharacteristic, complemented
279#877—104no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5C22×D311yescharacteristic
289C23×D5—22no—
290C23×D5—22no—
291C23×D5—22no—
292C23×D5—22no—
293C23×D5—41no—
294C23×D5—41no—
295C23×D5C4×D314yes—
296C23×D5C22×D311yescharacteristic
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5—62no—
303C22×C4×C5—62no—
304C22×C4×C5—121no—
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C22×Dic5—31no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5—62no—
312C22×Dic5—62no—
313C22×Dic5—121no—
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C2×C4×D5—34no—
317C2×C4×D5—34no—
318C2×C4×D5—62no—
319C2×C4×D5—62no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C22⋊C4—22no—
323C5×C22⋊C4—34no—
324C42×C5—62no—
325C42×C5—121no—
326C22⋊Dic5—22no—
327C22⋊Dic5—34no—
328#685—22no—
329#685—22no—
330#685—34no—
331#685—34no—
332#685—34no—
333#685—41no—
334#685—41no—
335#685—62no—
336#685—62no—
337#685—62no—
338#683—62no—
339#683—62no—
340#683—121no—
341#683—121no—
342C4×Dic5—62no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—151no—
348#388—151no—
349#388—151no—
350#388—151no—
351#385—151no—
352#385—151no—
353#381—151no—
354#380—151no—
355#379—51no—
356C4×C22⋊C4—31no—
357C4×C22⋊C4—151no—
358C4×C22⋊C4—151no—
359C22×C3×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5#11714yescomplemented
366C22×C3×C5C23×C411yescharacteristic
367C22×C3×C5C22×D411yescharacteristic
368C22×C3×C5C2×#4111yescharacteristic
369C22×C3×C5C2×#4111yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C2×C3×D5—22no—
374C2×C3×D5—22no—
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—416no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5C4×D414yes—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390Dic15—22no—
391Dic15—22no—
392Dic15—22no—
393Dic15—41no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C5×Dic3—22no—
397C5×Dic3—22no—
398C5×Dic3—22no—
399C5×Dic3—41no—
400C24×C3—51no—
401C24×C3—51no—
402C24×C3—54no—
403C24×C3—102no—
404C24×C3—102no—
405C24×C3—102no—
406C24×C3—102no—
407C24×C3—201no—
408C24×C3—201no—
409C24×C3C22×D511yescharacteristic
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4C22×D511yescharacteristic
413C22×C3×C4C22×D511yescharacteristic
414C22×Dic3—22no—
415C22×Dic3—22no—
416C22×Dic3—41no—
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3—51no—
420C22×Dic3—54no—
421C22×Dic3—54no—
422C22×Dic3—51no—
423C22×Dic3—102no—
424C22×Dic3—102no—
425C22×Dic3—102no—
426C22×Dic3—102no—
427C22×Dic3—201no—
428C22×Dic3—201no—
429C22×Dic3—201no—
430C22×Dic3C22×D511yescharacteristic
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C22×Dic3C22×D511yescharacteristic
434C3×C22⋊C4—22no—
435C3×C22⋊C4—102no—
436C3×C22⋊C4—102no—
437C3×C22⋊C4—102no—
438C3×C22⋊C4—201no—
439C3×C22⋊C4—201no—
440#217—54no—
441#217—54no—
442#217—54no—
443#217—54no—
444#217—102no—
445#217—102no—
446#217—102no—
447#217C4×D514yes—
448Dic3⋊C4—102no—
449Dic3⋊C4—102no—
450Dic3⋊C4—201no—
451Dic3⋊C4—201no—
452C4×Dic3—22no—
453C4×Dic3—41no—
454C4×Dic3—102no—
455C4×Dic3—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5C2×C4×D312yes—
461C23×C5#23712yes—
462C23×C5#23712yes—
463C23×C5C23×D311yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—28no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—21no—
472C22×D5—21no—
473C22×D5—21no—
474C22×D5—21no—
475C22×D5—28no—
476C22×D5—44no—
477C22×D5—44no—
478C22×D5—44no—
479C22×D5—44no—
480C22×D5—44no—
481C22×D5C2×C4×D312yes—
482C22×D5C2×C4×D312yes—
483C22×D5D3×D412yes—
484C22×D5#23712yes—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5—32no—
492C2×C4×C5—32no—
493C2×C4×C5—32no—
494C2×C4×C5—61no—
495C2×C4×C5—61no—
496C2×C4×C5—61no—
497C2×C4×C5—61no—
498C2×C4×C5—61no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5—61no—
502C2×C4×C5—61no—
503C2×C4×C5—124no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—32no—
511C2×Dic5—32no—
512C2×Dic5—32no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5—61no—
521C2×Dic5—61no—
522C2×Dic5—124no—
523C4×D5—68no—
524C4×D5—124no—
525C25—51no—
526C23×C4—31no—
527C23×C4—151no—
528C23×C4—151no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—51no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—158no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4—151no—
545C2×C22⋊C4—151no—
546C2×C22⋊C4—151no—
547C2×C22⋊C4—151no—
548C2×C22⋊C4—151no—
549C2×C22⋊C4—304no—
550C2×C22⋊C4D3×D511yescharacteristic
551C2×C42—31no—
552C2×C42—31no—
553C2×C42—151no—
554C2×C42—151no—
555#95—31no—
556#95—31no—
557#95—151no—
558#95—151no—
559#95—151no—
560#95—151no—
561#95—151no—
562#95—151no—
563C2×C3×C5—24no—
564C2×C3×C5C2×#11711yescharacteristic
565C2×C3×C5C2×C4×D411yescharacteristic
566C2×C3×C5#51811yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#54611yescharacteristic
569C2×C3×C5#55111yescharacteristic
570C2×C3×C5#55111yescharacteristic
571C3×D5—24no—
572C3×D5—42no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—52no—
578C23×C3—52no—
579C23×C3—52no—
580C23×C3—52no—
581C23×C3—108no—
582C23×C3—101no—
583C23×C3—101no—
584C23×C3—101no—
585C23×C3—101no—
586C23×C3—101no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—108no—
593C23×C3—204no—
594C23×C3—204no—
595C23×C3—204no—
596C23×C3—204no—
597C23×C3—204no—
598C23×C3C2×C4×D512yes—
599C23×C3#70912yes—
600C23×C3#70912yes—
601C23×C3C23×D511yescharacteristic
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—44no—
624C2×Dic3—52no—
625C2×Dic3—52no—
626C2×Dic3—52no—
627C2×Dic3—108no—
628C2×Dic3—101no—
629C2×Dic3—101no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—204no—
638C2×Dic3—204no—
639C2×Dic3C2×C4×D512yes—
640C2×Dic3C2×C4×D512yes—
641C2×Dic3D4×D512yes—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—22no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5#87714yescomplemented
649C22×C5C22×C4×D311yescharacteristic
650C22×C5C2×D3×D411yescharacteristic
651C22×C5C2×#23711yescharacteristic
652C22×C5C2×#23711yescharacteristic
653C22×C5C2×#23711yescharacteristic
654C22×C5#100411yescharacteristic
655C22×C5#100411yescharacteristic
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—22no—
665C2×D5—416no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5#67⋊C414yes—
671C4×C5—41no—
672C4×C5—41no—
673C4×C5—62no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—121no—
677Dic5—41no—
678Dic5—41no—
679Dic5—62no—
680Dic5—62no—
681Dic5—62no—
682Dic5—121no—
683C24—51no—
684C24—51no—
685C24—54no—
686C24—102no—
687C24—102no—
688C24—102no—
689C24—102no—
690C24—201no—
691C24—201no—
692C24C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—62no—
700C22×C4—62no—
701C22×C4—121no—
702C22×C4—154no—
703C22×C4—154no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—302no—
709C22×C4—302no—
710C22×C4—302no—
711C22×C4—302no—
712C22×C4—601no—
713C22×C4—601no—
714C22×C4—601no—
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—302no—
718C4⋊C4—302no—
719C4⋊C4—601no—
720C4⋊C4—601no—
721C22⋊C4—22no—
722C22⋊C4—34no—
723C22⋊C4—102no—
724C22⋊C4—102no—
725C22⋊C4—102no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—201no—
731C22⋊C4—201no—
732C22⋊C4—302no—
733C22⋊C4—302no—
734C22⋊C4—302no—
735C42—62no—
736C42—121no—
737C42—302no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—54no—
747C22×C3—102no—
748C22×C3—102no—
749C22×C3—102no—
750C22×C3—102no—
751C22×C3—102no—
752C22×C3—102no—
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—2016no—
757C22×C3—201no—
758C22×C3—201no—
759C22×C3—201no—
760C22×C3—201no—
761C22×C3#401814yescomplemented
762C22×C3C22×C4×D511yescharacteristic
763C22×C3C2×#70911yescharacteristic
764C22×C3C2×#70911yescharacteristic
765C22×C3C2×D4×D511yescharacteristic
766C22×C3#414411yescharacteristic
767C22×C3D5×#4111yescharacteristic
768C22×C3#414911yescharacteristic
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—201no—
772C3×C4—201no—
773Dic3—22no—
774Dic3—22no—
775Dic3—22no—
776Dic3—41no—
777Dic3—102no—
778Dic3—102no—
779Dic3—102no—
780Dic3—201no—
781C2×C5—24no—
782C2×C5C2×#87711yescharacteristic
783C2×C5C2×#67⋊C411yescharacteristic
784C2×C5#548611yescharacteristic
785C2×C5#558711yescharacteristic
786C2×C5#558711yescharacteristic
787C2×C5#559111yescharacteristic
788C2×C5#559111yescharacteristic
789D5—24no—
790D5—42no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—52no—
796C23—52no—
797C23—52no—
798C23—52no—
799C23—108no—
800C23—101no—
801C23—101no—
802C23—101no—
803C23—101no—
804C23—108no—
805C23—101no—
806C23—101no—
807C23—101no—
808C23—101no—
809C23—101no—
810C23—101no—
811C23—204no—
812C23—204no—
813C23—204no—
814C23—204no—
815C23—204no—
816C23#676512yes—
817C23C4×D3×D512yes—
818C23#677912yes—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—101no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—124no—
845C2×C4—152no—
846C2×C4—152no—
847C2×C4—152no—
848C2×C4—308no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—301no—
857C2×C4—301no—
858C2×C4—604no—
859C2×C4—604no—
860C2×C3—24no—
861C2×C3—104no—
862C2×C3—202no—
863C2×C3C2×#401811yescharacteristic
864C2×C3#6582411yescharacteristic
865C2×C3#6586111yescharacteristic
866C2×C3C4×D4×D511yescharacteristic
867C2×C3#6587911yescharacteristic
868C2×C3#6588411yescharacteristic
869C2×C3#6589011yescharacteristic
870C5#7382211yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—54no—
878C22—102no—
879C22—102no—
880C22—102no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—102no—
886C22—102no—
887C22—2016no—
888C22—201no—
889C22—201no—
890C22—201no—
891C22—201no—
892C22#9139314yescomplemented
893C22C2×#676511yescharacteristic
894C22C2×C4×D3×D511yescharacteristic
895C22D3×D4×D511yescharacteristic
896C22D5×#23711yescharacteristic
897C22#9202511yescharacteristic
898C22#9202611yescharacteristic
899C22C2×#677911yescharacteristic
900C4—41no—
901C4—41no—
902C4—62no—
903C4—62no—
904C4—62no—
905C4—121no—
906C4—201no—
907C4—201no—
908C4—302no—
909C4—302no—
910C4—302no—
911C4—601no—
912C3#1060530511yescharacteristic, complemented, Sylow
913C2—24no—
914C2—104no—
915C2—202no—
916C2#1175291611yescharacteristic
917C2#1175307011yescharacteristic
918C2D5×#67⋊C411yescharacteristic
919C2#1175320011yescharacteristic
920C2C2×#9139311yescharacteristic
921C2#1175476411yescharacteristic
922C2#1175483611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#91393C2semidirect
4. #11751047C2semidirect
5. C5×Dic3×C22⋊C4C2semidirect
7. #11749512C2semidirect
8. #11749487C2semidirect
9. #11748885C2semidirect
10. Dic3×#685C2semidirect
11. #11748871C2semidirect
12. #11748708C2semidirect
13. #11748707C2semidirect
14. #11748706C2semidirect
15. #11748705C2semidirect
24. C2×#6712C22semidirect
25. C2×#6712C22semidirect
27. C2×C4×C5×Dic3C22semidirect
28. C2×C4×C5×Dic3C22semidirect
34. D5×#217C4semidirect
35. C2×#6669C22semidirect
36. C2×#6669C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
103. C2×D5×Dic3C2×C4semidirect
104. C2×D5×Dic3C2×C4semidirect
122. #6665C2×C4semidirect
123. #6665C2×C4semidirect
141. Dic3×C22⋊C4D5semidirect
277. C2×C4×Dic3C2×D5semidirect
278. C2×C4×Dic3C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
365. C22×C3×C5#117semidirect
648. C22×C5#877semidirect
739. C3×C5#2342semidirect
761. C22×C3#4018semidirect
870. C5#73822semidirect
892. C22#91393semidirect
912. C3#10605305semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D5×#2172
C22×#66652
C2×#913932
#117510472
C5×Dic3×C22⋊C42
C3×#652442
#117495122
#117494872
#117488852
Dic3×#6852
#117488712
#117487082
#117487072
#117487062
#117487052
#106053053
#738225